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There are many different ways of registering or time-limiting software. If you want to know how a specific application does it, you will have to ask that application's creator.

The Windows registry is a disk file, there is no conceptual difference between storing data in the registry and another disk file. If you want to use a file to prevent an application from continuing, you must check this file at the point the software "continues" and stop. You must write something to the file when you want the application to stop "continuing".

The standard place to store application preferences on Mac OS X is ~/Preferences/application name, but this is just a standard, there is no requirement to store data there.